Question: Why wouldn't Justus of Tiberius or Philo of Alexandria mentioned something about Jesus in their writings?
AP: First, the work of Justus of Tiberias has been lost. Therefore, we do not really know if he dedicated any space to Jesus of Nazareth.
Second, the reason that Philo did not mention anything about Jesus is quite easy to explain and understand. Jesus was not as huge of a personality as the Gospels present. Remember how they talk about large crowds turning out to follow him. Sometimes they chased him from city to another. Sometimes the crowds were so large that he couldn't get out of his boat. Actually though, for the Roman Empire, also for the chiefs of the Jews, and even those living within Jerusalem in particular, Jesus was nothing more than an unimportant figure, just like a couple of rabbis of his day who also went unnoticed––Hanini ben Dosa or Honi the Circle Drawer. These two individuals show great similarities with Jesus: They were craftsmen, teachers of the Law, doers of certain miracles. However, they are not quoted by Philo of Alexandria, who had minimal interest in Galilee.
To this we should remember, as I have emphasized on many occasions, that there were many (some eleven or twelve) Messianic pretenders since the death of Herod the Great (4 BC) until the beginning of the First Great Revolution of the Jews against Rome. And we don't know their names either.
TWH: I wouldn't be surprised if Justus of Tiberias did write something about Jesus in his writings. He was a historian, like Josephus who included some comments about Jesus––especially the Testimonium Flavianum. Unfortunately, we will probably never know. That paragraph in Josephus, by the way, is hardly the focus of his text. It constitutes only a sliver of the larger work. Josephus, we should mention, recorded that Jesus "won over many of the Jews and many of the Greeks." It would be hard to call Jesus insignificant based on that witness and on the testimony of the Gospels. Questers for the historical Jesus love to toss out details of Jesus' ministry (or shrink them down)––especially the miracles––but those discourses mentioning all of the attention that Jesus received from Jerusalem (e.g., men being sent out to watch Jesus and report on his activities) and the attention he received while in Jerusalem (e.g., flipping over the tables in the temple; fielding questions from the Pharisees and the Sadducees) would have to get thrown out as well. I'm not sure how you do that, or even how you could shrink them down.
Concerning Philo, I would say there were two factors: (1) Philo's focus, and (2) Jesus' renown had not spread, in a significant way, outside of Israel's boundaries. There is no indication, for example, that someone came from beyond Israel to hear Jesus teach or to heal someone (though you'll read about stuff like that in the apocryphal Gospels). And Philo was connected to the ruling class in Jerusalem. Sure he had contact with Israel––both Galilee and Jerusalem. That's true. But given the people that he was connected to, it would make a lot of sense why he wouldn't mention Jesus––the one who had been causing his friends and family so much trouble.